Modern oil field operations demand a great quantity of information relating to the parameters and conditions encountered downhole. Such information typically includes characteristics of the earth formations traversed by the borehole, and data relating to the size and configuration of the borehole itself. The collection of information relating to conditions downhole, which commonly is referred to as “logging,” can be performed by several methods including wireline logging, logging while drilling (LWD), drillpipe conveyed logging, and coil tubing conveyed logging.
An important component of the well logging suite is the measurement of electrical properties of a reservoir formation. Some of these measurements are related to the resistivity or conductivity of the formation, and can be obtained by using a focused electrode device as a logging tool. Electrical properties of the formation are useful for finding water-filled porosity, and water saturation can be computed if formation porosity is known. If multiple water saturation measurements are available (e.g., from different types of logging tools), it becomes possible to measure characteristics of the flushed zone. In order to evaluate formation resistivity or conductivity, the focused electrode devices may measure the admittance of formation, i.e., a ratio of a measured electrical current to an applied voltage. After that, an inversion scheme can be conducted to retrieve resistivity or conductivity from the measured admittance.
Skin effect is the tendency of an alternating electrical current (AC) to become distributed within a conductor (e.g., the focused electrode device used as a logging tool), such that the electrical current density is largest near the surface of the conductor and decreases with greater depths in the conductor. Therefore, the electrical current flows mainly at the “skin” or surface of the conductor, between the outer surface and a level called the skin depth. Because of the skin effect, the relation between the conductivity (or resistivity) and admittance can be a complicated nonlinear function, especially for high conductivity region and deep measurements.
Since an accurate analytical model for the skin effect is not available, the conventional inversion method usually involves building a large database of admittance values for different formation depths and then performing interpolation or extrapolation to obtain conductivity/resistivity of the formation. However, this method has several flaws: very dense sampling is required to enhance the accuracy of the conventional inversion method, especially for the nonlinear region (i.e., high conductivity and deep measurements); the dense sampling not only increases the cost of building the database, but also degrades the efficiency of inversion. Furthermore, certain error is introduced to the inversion as a consequence of interpolation and extrapolation, since such inversion method, either being linear, Lagrange or spline, is not based on physics.